TY - JOUR
T1 - Hopf bifurcation of a two-neuron network with different discrete time delays
AU - Li, Shaowen
AU - Liao, Xiaofeng
AU - Li, Chunguang
AU - Wong, Kwok-Wo
PY - 2005/5
Y1 - 2005/5
N2 - In this paper, a two-neuron network with different time delays is investigated. By analyzing the associated characteristic equation, we obtain the conditions for delay-dependent and delay-independent asymptotic stability, respectively. Furthermore, we find that if the delay is used as a bifurcation parameter, Hopf bifurcation would occur. The direction and stability of the bifurcating periodic solutions are determined by using the Nyquist criterion and the graphical Hopf bifurcation theorem. Some examples are included to illustrate our results. © World Scientific Publishing Company.
AB - In this paper, a two-neuron network with different time delays is investigated. By analyzing the associated characteristic equation, we obtain the conditions for delay-dependent and delay-independent asymptotic stability, respectively. Furthermore, we find that if the delay is used as a bifurcation parameter, Hopf bifurcation would occur. The direction and stability of the bifurcating periodic solutions are determined by using the Nyquist criterion and the graphical Hopf bifurcation theorem. Some examples are included to illustrate our results. © World Scientific Publishing Company.
KW - Graphical hopf bifurcation theorem
KW - Hopf bifurcation
KW - Neural networks
KW - Stability
KW - Time delays
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U2 - 10.1142/S0218127405012879
DO - 10.1142/S0218127405012879
M3 - RGC 21 - Publication in refereed journal
SN - 0218-1274
VL - 15
SP - 1589
EP - 1601
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
IS - 5
ER -